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Dynamic Monte Carlo Method
In chemistry, dynamic Monte Carlo (DMC) is a Monte Carlo method for modeling the dynamic behaviors of molecules by comparing the rates of individual steps with random numbers. It is essentially the same as Kinetic Monte Carlo. Unlike the Metropolis Monte Carlo method, which has been employed to study systems at equilibrium, the DMC method is used to investigate non-equilibrium systems such as a reaction, diffusion, and so-forth (Meng and Weinberg 1994). This method is mainly applied to analyze adsorbates' behavior on surfaces. There are several well-known methods for performing DMC simulations, including the First Reaction Method (FRM) and Random Selection Method (RSM). Although the FRM and RSM give the same results from a given model, the computer resources are different depending on the applied system. In the FRM, the reaction whose time is minimum on the event list is advanced. In the event list, the tentative times for all possible reactions are stored. After the selection ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a Chemical reaction, reaction with other Chemical substance, substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both Basic research, basic and Applied science, applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the properties ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of ris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and ''molecule'' is often used when referring to polyatomic ions. A molecule may be homonuclear, that is, it consists of atoms of one chemical element, e.g. two atoms in the oxygen molecule (O2); or it may be heteronuclear, a chemical compound composed of more than one element, e.g. water (two hydrogen atoms and one oxygen atom; H2O). In the kinetic theory of gases, the term ''molecule'' is often used for any gaseous particle regardless of its composition. This relaxes the requirement that a molecule contains two or more atoms, since the noble gases are individual atoms. Atoms and complexes connected by non-covalent interactions, such as hydrogen bonds or ionic bonds, are typically not consid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Number Generation
Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but unpredictable to foresight. True random number generators can be '' hardware random-number generators'' (HRNGS) that generate random numbers, wherein each generation is a function of the current value of a physical environment's attribute that is constantly changing in a manner that is practically impossible to model. This would be in contrast to so-called "random number generations" done by ''pseudorandom number generators'' (PRNGs) that generate numbers that only look random but are in fact pre-determined—these generations can be reproduced simply by knowing the state of the PRNG. Various applications of randomness have led to the development of several different metho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinetic Monte Carlo
The kinetic Monte Carlo (KMC) method is a Monte Carlo method computer simulation intended to simulate the time evolution of some processes occurring in nature. Typically these are processes that occur with known transition rates among states. It is important to understand that these rates are inputs to the KMC algorithm, the method itself cannot predict them. The KMC method is essentially the same as the dynamic Monte Carlo method and the Gillespie algorithm. Algorithms One possible classification of KMC algorithms is as rejection-KMC (rKMC) and rejection-free-KMC (rfKMC). Rejection-free KMC A rfKMC algorithm, often only called KMC, for simulating the time evolution of a system, where some processes can occur with known rates r, can be written for instance as follows: # Set the time t = 0. # Choose an initial state ''k''. # Form the list of all N_k possible transition rates in the system r_, from state ''k'' into a generic state ''i''. States that do not communicate wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metropolis Monte Carlo
A metropolis () is a large city or conurbation which is a significant economic, political, and cultural center for a country or region, and an important hub for regional or international connections, commerce, and communications. A big city belonging to a larger urban agglomeration, but which is not the core of that agglomeration, is not generally considered a metropolis but a part of it. The plural of the word is ''metropolises'', although the Latin plural is ''metropoles'', from the Greek ''metropoleis'' (). For urban centers outside metropolitan areas that generate a similar attraction on a smaller scale for their region, the concept of the regiopolis ("regio" for short) was introduced by urban and regional planning researchers in Germany in 2006. Etymology Metropolis (μητρόπολις) is a Greek word, coming from μήτηρ, ''mḗtēr'' meaning "mother" and πόλις, ''pólis'' meaning "city" or "town", which is how the Greek colonies of antiquity referred to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Equilibrium
In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. This state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as dynamic equilibrium. Historical introduction The concept of chemical equilibrium was developed in 1803, after Berthollet found that some chemical reactions are reversible. For any reaction mixture to exist at equilibrium, the rates of the forward and backward (reverse) reactions must be equal. In the following chemical equation, arrows point both ways to indicate equilibrium. A and B are reactant chemical species, S and T are p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Reaction
A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the Atomic nucleus, nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive Chemical element, elements where both electronic and nuclear changes can occur. The substance (or substances) initially involved in a chemical reaction are called reagent, reactants or reagents. Chemical reactions are usually characterized by a chemical change, and they yield one or more Product (chemistry), products, which usually have properties different from the reactants. Reactions often consist of a sequence o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. The concept of diffusion is widely used in many fields, including physics (particle diffusion), chemistry, biology, sociology, economics, and finance (diffusion of people, ideas, and price values). The central idea of diffusion, however, is common to all of these: a substance or collection undergoing diffusion spreads out from a point or location at which there is a higher concentration of that substance or collection. A gradient is the change in the value of a quantity, for example, concentration, pressure, or temperature with the change in another variable, usually distance. A change in c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Resource
In computational complexity theory, a computational resource is a resource used by some computational models in the solution of computational problems. The simplest computational resources are computation time, the number of steps necessary to solve a problem, and memory space, the amount of storage needed while solving the problem, but many more complicated resources have been defined. A computational problem is generally defined in terms of its action on any valid input. Examples of problems might be "given an integer ''n'', determine whether ''n'' is prime", or "given two numbers ''x'' and ''y'', calculate the product ''x''*''y''". As the inputs get bigger, the amount of computational resources needed to solve a problem will increase. Thus, the resources needed to solve a problem are described in terms of asymptotic analysis, by identifying the resources as a function of the length or size of the input. Resource usage is often partially quantified using Big O notation. Com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computation Time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expressed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Memory
In computing, memory is a device or system that is used to store information for immediate use in a computer or related computer hardware and digital electronic devices. The term ''memory'' is often synonymous with the term ''primary storage'' or '' main memory''. An archaic synonym for memory is store. Computer memory operates at a high speed compared to storage that is slower but less expensive and higher in capacity. Besides storing opened programs, computer memory serves as disk cache and write buffer to improve both reading and writing performance. Operating systems borrow RAM capacity for caching so long as not needed by running software. If needed, contents of the computer memory can be transferred to storage; a common way of doing this is through a memory management technique called ''virtual memory''. Modern memory is implemented as semiconductor memory, where data is stored within memory cells built from MOS transistors and other components on an integrated c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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